Conformal Prediction Regions are Imprecise Highest Density Regions
This work is significant for researchers in the field of Imprecise Probability and Conformal Prediction, as it provides a new connection between two important theories, although it appears to be an incremental contribution.
The authors found that Conformal Prediction Regions are equivalent to Imprecise Highest Density Regions under certain assumptions, establishing a new relationship between Conformal Prediction and Imprecise Probability theories. This result does not provide specific numbers or metrics.
Recently, Cella and Martin proved how, under an assumption called consonance, a credal set (i.e. a closed and convex set of probabilities) can be derived from the conformal transducer associated with transductive conformal prediction. We show that the Imprecise Highest Density Region (IHDR) associated with such a credal set corresponds to the classical Conformal Prediction Region. In proving this result, we establish a new relationship between Conformal Prediction and Imprecise Probability (IP) theories, via the IP concept of a cloud. A byproduct of our presentation is the discovery that consonant plausibility functions are monoid homomorphisms, a new algebraic property of an IP tool.